SC-LDPC Encoding with Base Matrix Decomposition for Low Error Rates

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Solution Overview

Problem

Current LTE turbo codes exhibit an error floor when the size of information increases, leading to high error rates, unnecessary data retransmissions, and increased complexity, which is inadequate for next-generation communication systems requiring ultra-reliable and low-latency radio.

Innovation Solution

A method for constructing a parity check matrix with a high degree of freedom for spatially coupled low-density parity-check (SC-LDPC) codes by decomposing a base matrix, spatially coupling decomposition matrices, generating a circulant shift value matrix, and applying lifting values to encode input signals, using algorithms like the Latin Square or progressive edge growth.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If LTE turbo code is used for channel coding, then communication service can be provided, but error rate increases and reliability decreases when information size increases

Engineering Contradiction:

Improveerror rateVSAvoidinformation size handling

Core Design Contradiction:

ReliabilityVSAdaptability or versatility

Solution Approach 1:

The base matrix of the LDPC-BC code is decomposed into multiple decomposition matrices (first, second, and third decomposition matrices). Each decomposition matrix processes a portion of the information bits independently, allowing the system to handle larger information sizes while maintaining error correction performance. The encoded bits from each decomposition matrix are then interleaved and combined to form the final codeword.

Inventive Principle:

Principle #1Segmentation

2Reliability

If complex channel coding is applied to reduce error rate, then reliability improves, but device complexity and computational load increase

Engineering Contradiction:

Improveerror rateVSAvoidcoding complexity

Core Design Contradiction:

ReliabilityVSDevice complexity

Solution Approach 1:

The encoding process is divided into multiple independent stages corresponding to different decomposition matrices. Each stage processes a subset of information bits through its own generator matrix, reducing the computational complexity of each individual encoding operation while maintaining overall coding performance through the combination of multiple stages.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent introduces a temporal dimension to the encoding process by processing information bits in multiple stages across different time slots or processing cycles. The first, second, and third decomposition matrices operate in sequence, with their outputs interleaved and combined. This multi-dimensional approach distributes computational load over time, reducing peak complexity requirements.

Inventive Principle:

Principle #17Another dimension (Dimensionality change)

3Reliability

If larger code size is used to improve reliability, then error rate decreases, but transmission latency and processing time increase

Engineering Contradiction:

Improveerror rateVSAvoidtransmission latency

Core Design Contradiction:

ReliabilityVSLoss of time

Solution Approach 1:

The information bits are divided into multiple groups that are processed in parallel through different decomposition matrices. The first decomposition matrix processes one group of information bits, the second decomposition matrix processes another group, and so on. This parallel processing structure reduces the overall encoding time compared to processing all information bits sequentially through a single large code.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The encoded bit sequences from multiple decomposition matrices are interleaved and combined to form the final codeword. This merging operation efficiently combines the results of parallel processing stages, achieving the reliability benefits of large codes while maintaining the speed advantages of smaller, parallel processing units.

Inventive Principle:

Principle #5Merging (Combining)

4Adaptability or versatility

If base matrix decomposition and multi-stage lifting is applied, then degree of freedom in parity check matrix construction increases, but encoding process complexity increases

Engineering Contradiction:

Improveparity check matrix construction flexibilityVSAvoidencoding process complexity

Core Design Contradiction:

Adaptability or versatilityVSDevice complexity

Solution Approach 1:

The base matrix is decomposed into multiple smaller decomposition matrices, each of which can be independently configured and optimized. This segmentation provides flexibility in designing the parity check matrix structure while keeping each individual decomposition matrix simple enough for efficient processing. The lifting operation is applied separately to each decomposition matrix, further enhancing design freedom without proportionally increasing complexity.

Inventive Principle:

Principle #1Segmentation

Data Source

PatentUS11271591B2SC-LDPC code encoding method and device therefor

Publication Date: 2022.03.08 LG ELECTRONICS INC

AI summary

Disclosed is an encoding method of a spatially coupled-low density parity Check (SC-LDPC) code of a terminal. The encoding method of the SC-LDPC code of the present disclosure can comprise: a step of generating a plurality of decomposition matrices by decomposing a base matrix of a preset LDPC block code. a step of generating a base matrix of the SC-LDPC code by spatially coupling the plurality of decomposition matrices in accordance with the termination length. a step of generating a circulant shift value matrix from the base matrix of the SC-LDPC code. a step of generating a plurality of lifting values for the base matrix of the SC-LDPC code. and a step for encoding an input signal by using a generator matrix defined by using of the base matrix of the SC-LDPC code, the circulant shift value matrix, and the plurality of lifting values.